This book is written particularly for mathematics students and, of
course, for mathematicians interested in set theory. Only some fun-
mental parts of naive set theory are presupposed, - not more than is
treated in a textbook on set theory, even if this restricts us only to
the most basic facts of this field. We have summarized all of this in
Chapter 0 without longer discusssions and explanations, because there
are s- eral textbooks which can be consulted by the reader, e.g.
HrbacekIJech [88], KneeboneIRotman [99], ShenIVereshchagin [159].
Besides this only elementary facts of analysis are used. The theory of
ordered sets can be divided into two parts, depending on whether the
sets under consideration are finite or infinite. The first part is
grounded mainly in combinatorics and graph theory and does not make
essential use of set-theorical concepts, whereas the second part
presupposes a knowledge of the fundamental notions of set theory, in
particular of the system of ordinal and cardinal numbers. In this book
we mainly deal with general infinite ordered sets. In this field the
textbook literature is still very small. Therefore this book supplements
the existing literature.